Question

C = 100 + 0.8 Yd

I = 500        X = 600         M = 650         T = 400

but G = G₀ - 0.05Y

G:400

What value of G0 would make income equal to the same value as in Q1? (Don't try to shortcut and just plug previous Y into the new equation for G, gotta solve the new AE equation.)

If Investment falls from 500 to 499, what is change in Y? (ie what is investment multiplier?)

Answer 1

Hi student,

I have answered all your questions. Please let me know if you have any query in the comments.

Answer –

The consumption function is : C = 100 + 0.8Y = 100 + 0.8(Y – T) = 100 + 0.8(Y – 400);

Investment (I) = 500;

Government expenditure (G) = 400;

Net Exports (X – M) = (600 – 650) = -50.

The equation for aggregate expenditure in Q1 : Y = C + I + G + (X – M)

or, Y= 100 + 0.8(Y – 400) + 500 + 400 – 50;

or, Y = 100 + 0.8Y – 320 + 500 + 400 – 50;

or, 0.2Y = 630

or, Y = 3150.

Now, suppose G = G0 – 0.05Y

Plugging the value of G again in the new AE equation, we get,

Y= 100 + 0.8(Y – 400) + 500 + G0 – 0.05Y – 50;

Or, 3150 = 100 + 0.8(3150 – 400) + 500 + G0 – 0.05*3150 – 50;

Or, 3150 = 2800 + G0 –207.5;

Or, G0 = 3150 – 2800 + 207.5;

Or, G0 = 557.5 i.e., G0 = 557.5 would make income equal to the same value as in Q1.

Now, let us consider the consumption function : C = 100 + 0.8(Y – 400).

Comparing it with the standard consumption function of C = a + bY, where b = marginal propensity to consume (MPC), we see that in our given question, MPC = 0.8.

Now, MPC + MPS = 1;

or, MPS = 1 – MPC = 1 – 0.8 = 0.2.

When I falls from 500 to 499, then ∆I = -1.

The value of Investment Multiplier is given as:

∆Y/∆I =1/ 1-MPC = 1/MPS

or, ∆Y/∆I = 1/0.2 = 5.

or, ∆Y = 5*(∆I) = 5*(-1) = -5.

Thus, Y would fall by 5 units from 3150 to 3145.

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